%INTEGRATION_BND_DIRECT%

surface integration of a scalar value along pieces of boundary

begin_alias{} "Alias1" = " ... IDENT%BND_wall% ... MAT$MaterialTag$ ... BC$BCindex$ ... POSTPROCESS$PostprocessTag1$ ... " # definition of Alias1 "Alias2" = " ... IDENT%BND_wall% ... MAT$MaterialTag$ ... BC$BCindex$ ... POSTPROCESS$PostprocessTag2$ ... " # definition of Alias2 end_alias INTEGRATION($IntInd$) = ( %INTEGRATION_BND_DIRECT%, ExpressionOfIntegrand, $PostprocessTag1$, $PostprocessTag2$, ... )

The POSTPROCESS-flags $PostprocessTag1$, $PostprocessTag2$, ... define the IntegrationArea. Their number is not limited. This computes the integral of a functional $ f$ (ExpressionOfIntegrand) with respect to the region $ \partial\Omega$ identified by the POSTPROCESS-flags

\begin{align} I_\text{BndDirect} = \int\limits_{\partial\Omega} f dA\end{align}

by a sum approximation

\begin{align} I_\text{BndDirect} \approx \sum_{i \in P_{Bnd}} f_i \cdot A_i,\end{align}

where $ P_{Bnd}$ is the set of all boundary points with the given POSTPROCESS-flags and $ A_i$ is the area of the i-th point. Example:

INTEGRATION($IntInd1$) = ( %INTEGRATION_BND_DIRECT%, [Y%ind_p%+Y%ind_p_dyn%], $PostprocessTag1$, $PostprocessTag2$, $PostprocessTag3$ ) INTEGRATION($IntInd2$) = ( %INTEGRATION_BND_DIRECT%, equn{$EqnName$}, $PostprocessTag1$, $PostprocessTag2$, $PostprocessTag3$ ) INTEGRATION($IntInd3$) = ( %INTEGRATION_BND_DIRECT%, curve{$CrvName$}depvar{%ind_DepVar%}, $PostprocessTag1$, $PostprocessTag2$, $PostprocessTag3$ )